Analysis of direct phase modulation with an injection-locked oscillator

The behaviour of low cost, direct phase modulators, based on injection-locked oscillators, is studied in detail, using a reduced-order semi-analytical formulation. The derived expressions allow the identification of critical design parameters, influencing aspects such as the sensitivity of the phase-shift interval versus the element tolerances or the amplitude modulation. An envelope-domain equation, derived from the same semi-analytical formulation, allows the understanding of qualitative changes in the modulator dynamics versus variations in the modulation frequency, in different operation conditions. The study is illustrated with a modulated push-push oscillator at 18 GHz. Very good agreement has been obtained between the theoretical results and the experimental measurements.